Israel on Sunday barred the Hebron governor from entering its territory after he visited the family of a Palestinian who killed a US-Israeli teenage girl in her sleep, officials said.

On Thursday, 19-year-old Mohammed Nasser Tarayra broke into the Jewish settlement of Kiryat Arba in the West Bank on the outskirts of Hebron and killed 13-year-old Israeli-American Hallel Yaffa Ariel before being shot dead by a security guard.

The murder sparked outrage and prompted Israel to lock down Hebron, a flashpoint city in the occupied Palestinian territory.

The decision to bar mayor Kamal Humeid from Israel was taken by COGAT, the Israeli defence ministry unit that manages civilian affairs for Palestinians in the West Bank and liaises with Gaza.

A statement said Humeid had paid a condolence visit to Tarayra's family and was therefore "barred from entering Israel" and that he had been stripped of "his privileges," without elaborating.

Humeid said on Facebook he does not enjoy any special privileges and has "no business in Israel" that would lead him to enter it.

A day after Thursday's attack, 48-year-old Israeli Michael Mark was killed after his car was fired on by a suspected Palestinian gunman south of Hebron.

Prime Minister Benjamin Netanyahu told the cabinet on Sunday that a series of measures had been taken "including aggressive ones which had not been used in the past" to respond to such attacks.

"This includes the lockdown of the entire Hebron district," home to 700,000 people, he said.

Netanyahu said the army had also revoked the Israeli work permits of residents of Beni Naim, home village of the Palestinian assailants.

Other measures, he said, include a "massive" bolstering of Israeli troops and an investigation into family members of Palestinian assailants "and their arrest if they were involved" in attacks.

On Friday a relative of Tarayra, 27-year-old Sarah Tarayra, was shot dead after drawing a knife on Israeli forces in Hebron.

Hebron has been one of the main focuses of a wave of deadly unrest that has rocked Israel and the Palestinian territories since October, with the army saying 80 of the attacks on Israelis were carried out by Palestinians from the Hebron area.

Several hundred Jewish settlers live in a tightly guarded enclave in the heart of the city of more than 200,000 Palestinians, a persistent source of tensions.

At least 214 Palestinians, 34 Israelis, two Americans, an Eritrean and a Sudanese have been killed since October.